An algorithm for the two dimensional FFT

Hoyer, Elmer A.; Berry, William L.

doi:10.1109/icassp.1977.1170190

Cited by 9 publications

(1 citation statement)

References 5 publications

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“…With this in mind, we can, for instance, convert the classical Cooley-Tukey algorithms [4] into relatively new split-algorithms (see [13]). Such a recasting is especially topical in dealing with multidimensional transforms [note that the reduction to one-dimensional transforms is known to be not the best way (see [7,8,12])]. Some approaches to the reconstruction of multidimensional Fourier transforms are demonstrated in [12].…”

Section: Pa(n+ir(n+i)) \)mentioning

confidence: 98%

The algorithm structure and V-matrices

Тыртышников¹

1994

Russian Journal of Numerical Analysis and Mathematical Modelling

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This is a brief survey devoted to K-matrices, which can be used not only for describing the structure of an algorithm but can also provide some additional information about it. We show the way K-matrices appear in such applications as the roundoff error analysis, the fast computation of gradients, and the complexity evaluation of linear algorithms. A perfectly simple procedure for deriving a fast algorithm for computing gradients is proposed. We also discuss some lower bounds for linear algorithms based on a determinant inequality obtained in the paper.Structural properties of algorithms form the basis for research in several directions that appear at first glance to be distantly related. We can name here at least three such directions: the roundoff error analysis, the fast computation of gradients, and the complexity evaluation of linear algorithms. So far, these areas have not been considered interrelated because there were no cross-references from one area to another. The goal of this paper is to show that there is a natural unifying basis for these areas, namely F-matrices. It should be emphasized that K-matrices fully reflect the informational structure of an algorithm.Our intention was to write a survey of K-matrices and their application to the analysis of algorithms. In Section 1 we give the definition of F-matrices and a sketch of their use in the roundoff error analysis. Sections 2 and 3 are devoted to some applications of F-matrices that make use of different augmentations of F-matrices.In Section 2 we consider a very simple procedure for deriving a fast algorithm for computing gradients. In Section 3 we primarily discuss lower bounds for linear algorithms that are based on a new determinant inequality, Appendix contains the proof of the inequality.

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